A train travels a distance of 600 km at a constant speed. If the speed of the train is increased by 5 km/h, the journey would take 4 hours less. Find the speed of the train.

Question: A train travels a distance of 600 km at a constant speed. If the speed of the train is increased by 5 km/h, the journey would take 4 hours less. Find the speed of the train.

Solution:
Let,
the speed of the train be x km/h

ATQ,
600/x - 600/(x + 5) = 4
⇒ {600(x + 5) - 600x}/x(x + 5) = 4
⇒ (600x + 3000 - 600x)/(x² + 5x) = 4
⇒ 3000/(x² + 5x) = 4
⇒ 4x² + 20x = 3000
⇒ 4x² + 20x - 3000 = 0
⇒ x² + 5x - 750 = 0
⇒ x² + 30x - 25x - 750 = 0
⇒ x(x + 30) - 25(x - 30) = 0
⇒ (x + 30)(x - 25) = 0
⇒ x = - 30 or 25
∴ x = 25 [neglecting the negative value of x]

∴ Speed of the train 25 km/h